Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.

With the prevalence of Internet access and online services, various big graphs are generated in many real applications (e.g., online social networks and knowledge graphs). An important task on analyzing and mining these graphs is keyword search. Essentially, given a graphGand queryQassociated with a set of keywords, the keyword search aims to find a substructure (e.g., rooted tree or subgraph)SinGsuch that nodes inScollectively cover part of or all keywords inQ, and in the meanwhile,Sis optimal on some user specified semantics. Keyword search on graphs can be applied in many real-life applications, such as point-of-interests recommendation and web search facility. In spite of the great importance of graph keyword search, we, however, notice that the latest survey on this topic is far out of date. Consequently, there is prompt need to conduct a comprehensive survey in this research direction. Motivated by this, in this survey, we systematically review graph keyword search studies by classifying the existing works into different categories according to the specific problem definition. This survey aims to provide the researchers a comprehensive understanding of existing graph keyword search solutions.

The requirement for appropriate ways to measure the similarity between data objects is a common but vital task in various domains, such as data mining, machine learning and so on. Driven by abundant real-world applications, many well-known similarity (distance) metrics are proposed to measure the pairwise similarity of data pairs, e.g., graph edit distance for graphs and dynamic time warping for time series. However, many similarity metrics suffer from the high time complexity. More specifically, most of the well-known similarity metrics often need quadratic time or even much more time to compute the ground truth similarity and some of them are proven to be NP-hard. With the development of deep learning techniques, there is an emerging research trend on the learning for similarity computation on various data types in the field of database (DB) and data mining, which is quite different with the metric learning studies in the machine learning (ML) literature. Specifically, the studies in the ML focus on the learning for semantic similarity in specific tasks, which is implicitly indicated by the training data, on the data in the feature space. While the studies in the DB literature usually consider the learning for well-defined similarity metrics (e.g., graph edit distance) on the data objects (e.g., graphs), such that it can benefit the similarity computation on data in terms of multiple aspects, such as computation time, metric quality and search heuristic, and the learned representation of data can also be naturally fed to downstream tasks. This survey paper provides a comprehensive review of similarity computation learning on several data types, including set, sequence and graph. Moreover, we first classify the learning-based approaches in terms of their learning target into three categories, i.e., similarity learning, cost matrix learning and search heuristic learning. Then we detail some representative approaches for each category on every data type, and analyze some key features that are utilized by these approaches. Finally, we discuss some challenges and future directions towards the learning for similarity learning on these data types.

In this paper, we study the problem of maximal biclique enumeration on large uncertain bipartite graphs. Given an uncertain bipartite graph $\mathcal{G}=(U,V,E,p)$ , a probability threshold $\tau$ , and two size constraints $\alpha$ and $\beta$ , we aim to efficiently enumerate all maximal $\tau$ -bicliques in $\mathcal{G}$ , where a maximal $\tau$ -biclique $B(L,R)$ is a complete subgraph of $\mathcal{G}$ with (1) the probability of B is no less than $\tau$ , (2) $|L| \ge \alpha$ and $|R| \ge \beta$ , and (3) $B$ is a maximal complete subgraph satisfying (1) and (2). This problem has many applications, such as biclustering of gene expression data, fraud detection, similar group identification, etc. Despite the wide range of applications, to the best of our knowledge, we note that there are no efficient and scalable solutions to this problem in the literature. This problem is computationally challenging due to its #P-completeness. In this paper, we propose a competitive branch-and-bound method, namely MBEN, which explores the search space in a depth-first manner with a variety of pruning techniques. To improve the performance of MBEN, we propose several novel and efficient search processing optimizations. First, we always select the side with fewer candidates to expand the search space. With this search strategy, we have a chance to prune the fruitless branches early. Second, we devise an advanced pruning technique by considering the size pruning and probability pruning at the same time to boost the pruning capacity. Last, we implement MBEN with pre-allocated arrays and pointer maintaining techniques such that the frequent work sets creating operations can be substituted by array element switching operations. In addition, we introduce useful graph reduction techniques to further accelerate the computation. Comprehensive performance studies on 10 real datasets demonstrate that our proposals can significantly outperform the baseline methods by more than two orders of magnitude.